Too many files? No problem – RAR them. You can do that now that there's an official RAR app on Android. This is a fabulously useful app on Windows, where it costs cash money. On Android, it appears to be completely free.
The RAR app for Android lets you create ZIP and RAR archives, but you can unpack RAR, ZIP, TAR, GZ, BZ2, XZ, 7z, ISO, ARJ archives. There are also options to repair damaged archives and it supports encryption for creating and unpacking archives. It even comes with device benchmarking.
The app isn't particularly lovely, but it follows the Android design guidelines with a minimum of clutter. There's a holo light theme that looks a little more modern, in my opinion. It's definitely something to look into on the basis of features alone.